5th International & 26th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12th–14th, 2014, IIT Guwahati, Assam, India
APPLICATION OF GENETIC ALGORITHM TO OPTIMIZE PROPERTIES OF PULSED CURRENT MICRO PLASMA ARC WELDED INCONEL 625 SHEETS Kondapalli Siva Prasad1*, Chalamalasetti Srinivasa Rao2, Damera Nageswara Rao3, Chintala Gopinath4 1*
Anil Neerukonda Institute of Technology & Sciences, Visakhapatnam, INDIA 2
AU College of Engineering, Andhra University, Visakhapatnam, INDIA 3
Centurion University of Technology & Management, Odisha, INDIA 4
Guru Nanak Institutions Technical Campus, Hyderabad, INDIA 1*
Corresponding Author Email:
[email protected] Abstract
Pulsed Current Micro Plasma Arc Welding (PCMPAW) is commonly used for joining thin sheets where Laser beam and Electron Beam welding are not economical. The quality of welded joint depends on the grain size, hardness and ultimate tensile strength, which have to be properly controlled and optimized to ensure better economy and desirable mechanical characteristics of the weld. This paper highlights the development of empirical mathematical equations using multiple regression analysis, correlating various welding parameters to grain size, hardness and ultimate tensile strength in PCMPAW of Inconel 625 sheets. The experiments were conducted based on a five factor, five level central composite rotatable design matrix. Genetic Algorithm (GA) is adopted to optimize the process parameters for achieving the desired grain size, hardness and ultimate tensile strength. Key Words: Inconel 625, pulsed current, Micro Plasma Arc Welding, Genetic Algorithm.
1
Introduction
The plasma welding process was introduced to the welding industry in 1964 as a method of bringing better control to the arc welding process in lower current ranges [1]. Today, plasma retains the original advantages it brought to the industry by providing an advanced level of control and accuracy to produce high quality welds in both miniature and pre precision applications and to provide long electrode life for high production requirements at all levels of amperage. Plasma welding is equally suited to manual and automatic applications. It is used in a variety of joining operations ranging from welding of miniature components to seam welding to high volume production welding and many others. According to Balasubramanian. M et al. (2010) and Balasubramanian. B et al. (2006) pulsed current MPAW involves cycling the welding
current at selected regular frequency. The maximum current is selected to give adequate penetration and bead contour, while the minimum is set at a level sufficient to maintain a stable arc. This permits arc energy to be used effectively to fuse a spot of controlled dimensions in a short time producing the weld as a series of overlapping nuggets. By contrast, in constant current welding, the heat required to melt the base material is supplied only during the peak current pulses allowing the heat to dissipate into the base material leading to narrower Heat Affected Zone (HAZ). Advantages include improved bead contours, greater tolerance to heat sink variations, lower heat input requirements, reduced residual stresses and distortion, refinement of fusion zone microstructure and reduced width of HAZ. There are four independent parameters that influence the process are peak current, back current, pulse and pulse width.
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APPLICATION OF GENETIC ALGORITHM TO OPTIMIZE PROPERTIES OF PULSED CURRENT MICRO PLASMA ARC WELDED INCONEL 625 SHEETS
In this investigation, experiments conducted using the design of experiments concept were used for developing mathematical models to predict such variables. Marimuthu K and Murugan N (2003) optimized weld bead geometry of plasma transferred arc hardfaced valve seat rings . Gunaraj V and Murugan N (1999) predicted and compared of the area of the heat affected zone for the beadon-plate and bead-on joint in SAW of pipes. According to Juang S C and Tarng Y S (2002) the desired welding process parameters are determined based on the experience of skilled workers or from the data available in the handbook. This does not ensure the formation of optimal or near optimal weld pool geometry. It has been proven by Allen TT et al .(2002) and Kim I-S et al. (2001) that efficient use of statistical design of experiment techniques and other optimization tools can impart scientific approach in welding procedure. These techniques can be used to achieve optimal or near optimal bead geometry from the selected process parameters. Kim D et al. (2005) reviewed that optimization using regression modeling, neural network, and Taguchi methods could be effective only when the welding process was set near the optimal conditions or at a stable operating range , but, near-optimal conditions cannot be easily determined through full-factorial experiments when the number of experiments and levels of variables are increased. Also, the method of steepest ascent based upon derivatives can lead to an incorrect direction of search due to the non-linear characteristics of the welding process. According to Kim D and Rhee S (2001), Genetic algorithm, being a global algorithm, can overcome the above problems associated with full-factorial experiments and the objective function to be optimized using GA need not be differentiable. In the present study, a sequential genetic algorithm has been used to optimize the process parameters and achieve minimum fusion zone grain size, maximum hardness and ultimate tensile strength of PCMPAW Inconel 625 sheets. 2
Experimental Procedure
Inconel 625 sheets of 100 x 150 x 0.25 mm are welded autogenously with square butt joint without edge preparation. The chemical composition Inconel 625 is given in Table 1. High purity argon gas (99.99%) is used as a shielding gas and a trailing gas right after welding to prevent absorption of oxygen and nitrogen from the atmosphere. The welding has been carried out under the welding conditions presented in Table 2. From the literature four important factors of pulsed current MPAW as presented in Table 3 are chosen. A large number of trail experiments were carried
out using 0.25 mm thick Inconel 625 sheets to find out the feasible working limits of pulsed current MPAW process parameters. Due to wide range of factors, it has been decided to use four factors, five levels, rotatable central composite design matrix to perform the number of experiments for investigation. Table 4 indicates the 31 set of coded conditions used to form the design matrix. For the convenience of recording and processing the experimental data, the upper and lower levels of the factors are coded as +2 and -2, respectively and the coded values of any intermediate levels can be calculated by using the expression -1 as described by Babu S et al. (2008). Xi = 2[2X-(Xmax + Xmin)] / (Xmax – Xmin)
(1)
where Xi is the required coded value of a parameter X. The X is any value of the parameter from Xmin to Xmax, where Xmin is the lower limit of the parameter and Xmax is the upper limit of the parameter. Table 1 Chemical composition of Inconel 625 (weight %) C 0.0300 Cr 20.8900 Ta
Mn 0.0800 Ni 61.6000 Ti
0.0050
0.1800
P 0.0050 Al 0.1700 N 0.0100
S 0.0004 Mo 8.4900 Co 0.1300
Si 0.1200 Cb 3.4400 Fe 4.6700
Table 2 Welding conditions Power source
Polarity Mode of operation Electrode Electrode Diameter Plasma gas Plasma gas flow rate Shielding gas Shielding gas flow rate Purging gas Purging gas flow rate Copper Nozzle diameter Nozzle to plate distance Welding speed Torch Position Operation type
Secheron Micro Plasma Arc Machine (Model: PLASMAFIX 50E) DCEN Pulse mode 2% thoriated tungsten electrode 1mm Argon & Hydrogen 6 Lpm Argon 0.4 Lpm Argon 0.4 Lpm 1mm 1mm 260mm/min Vertical Automatic
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5th International & 26th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12th–14th, 2014, IIT Guwahati, Assam, India
Table 3 Important factors and their levels 3.2 SI No. 1 2 3 4
Input Factor Peak Current Back Current Pulse rate Pulse width
Units
-2
Levels -1 0
Amperes
6
6.5
7
7.5
8
Amperes
3
3.5
4
4.5
5
Pulses/ Second %
20
30
40
50
60
30
40
50
60
70
+1
+2
Table 4 Design matrix and experimental results Serial Peak Back Pulse Pulse Grain Hardness Ultimate No Current current rate width Size (VHN) Tensile Strength(UTS) (Amperes) (Amperes) (Pulses/ (%) (Micons) (MPa) Second) 1 -1 -1 -1 -1 40.812 267 833 2 1 -1 -1 -1 50.226 260 825 3 -1 1 -1 -1 41.508 269 838 4 1 1 -1 -1 47.536 263 826 5 -1 -1 1 -1 47.323 263 826 6 1 -1 1 -1 45.206 265 830 7 -1 1 1 -1 45.994 265 825 8 1 1 1 -1 43.491 266 826 9 -1 -1 -1 1 46.290 264 825 10 1 -1 -1 1 49.835 260 820 11 -1 1 -1 1 40.605 268 835 12 1 1 -1 1 47.764 263 828 13 -1 -1 1 1 50.095 260 818 14 1 -1 1 1 46.109 264 826 15 -1 1 1 1 47.385 263 824 16 1 1 1 1 45.013 265 830 17 -2 0 0 0 40.788 266 830 18 2 0 0 0 45.830 265 826 19 0 -2 0 0 51.663 258 821 20 0 2 0 0 47.263 265 828 21 0 0 -2 0 45.270 265 832 22 0 0 2 0 46.030 264 825 23 0 0 0 -2 44.626 266 831 24 0 0 0 2 46.626 264 825 25 0 0 0 0 44.845 266 830 26 0 0 0 0 44.845 266 830 27 0 0 0 0 40.145 270 840 28 0 0 0 0 44.845 266 830 29 0 0 0 0 40.045 272 838 30 0 0 0 0 44.845 266 830 31 0 0 0 0 40.445 266 834
3 3.1
Recording the Responses Measurement of grain size
Sample preparation and mounting is done as per ASTM E 3-1 standard. The samples are surface grounded using sand paper and further polished by using aluminum oxide initially and the by utilizing diamond paste and velvet cloth in a polishing machine. The polished specimens are etched by using Aqua regia solution to reveal the microstructure as per ASTM E407.
Measurement of hardness
Vickers’s micro hardness testing machine (Make: METSUZAWA CO LTD, JAPAN, Model: MMT-X7) was used to measure the hardness at the weld fusion zone by applying a load of 0.5Kg as per ASTM E384. Average values of three samples of each test case are presented in Table 4. 3.3 Measurement Strength
of
Ultimate
Tensile
Three transverse tensile specimens are prepared as per ASTM E8M-04 guidelines and the specimens after wire cut Electro Discharge Machining are shown in Fig.2. Tensile tests are carried out in 100kN computer controlled Universal Testing Machine (ZENON, Model No: WDW-100). The specimen is loaded at a rate of 1.5kN/min as per ASTM specifications, so that the tensile specimens undergo deformation. From the stress strain curve, the ultimate tensile strength of the weld joints is evaluated and the average of three results is presented in Table 4. 4
Developing Mathematical Models
A second order polynomial equation used to represent the response surface ‘Y’ is given by Montgomery D.C, (1991) : Y = bo+∑bi xi +∑βiixi2 + ∑∑bijxixj+∈
(2)
Using MINITAB 14 statistical software package, the significant coefficients were determined and final model is developed using significant coefficients to estimate grain size, hardness and ultimate tensile strength values of weld joint. The final mathematical model are given by Grain Size (G) G = 42.859+1.052X11.058X2+0.3150X3+0.625X4+1.640X22-2.320X1X3 (3) Hardness (H) H = 267.429-0.6258X1+1.375X2-0.208X3-0.625X41.493X22+1.937X1X3 (4) Ultimate tensile strength (T) T = 833.143-0.875X1+1.792X2-1.625X3-1.458X41.296X12-2.171X22-1.296X42+3.187X1X3 (5)
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APPLICATION OF GENETIC ALGORITHM TO OPTIMIZE PROPERTIES OF PULSED CURRENT MICRO PLASMA ARC WELDED INCONEL 625 SHEETS
where X1, X2, X3 and X4 are the coded values of peak current, back current, pulse rate and pulse width. The adequacy of the developed models was tested using the analysis of variance technique (ANOVA) and found to be adequate at 99% confidence level. The value of co-efficient of determination ‘ R2 ’ for the above developed models is found to be about 0.85 . 5. 5.1
Optimization Procedure Working Principle of GA
GA simulates the survival of the fittest among individuals over consecutive generation for solving a problem. Each generation consists of a population of characters. Each individual represent a point in a search space and a possible solution. The individuals in the population are then made to go through a process of evolution. The basic concept of GA is to encode a potential solution to a problem as a series of parameters. A single set of parameter value is termed as the genome of an individual solution. According to Palaniswamy P et al . (2007 and Asokan N et al. (2005) an initial population of individuals is generated randomly. In every generation the individuals in the current population are decoded according to a fitness function. The chromosomes with the highest population fitness are selected for mating. The genes of the parameters are allowed to exchange to produce new ones. These new ones then replace the earlier ones in the next generation. Thus the old population is discarded and the new population becomes the current population. The current population is checked for acceptability or solution. The iteration is stopped after the completion of maximum number of generations or on the attainment of the best results. The number of generations is continued till the termination criterion is achieved. The parameters used in GA are presented in Table 6. Table 6 Parameters used in GA
1 2 3 4 5
Sample size Crossover probability Mutation probability Number of generations Type of crossover
Grain Size
Hardness
30 0.7
40 0.96
Ultimate tensile Strength 40 0.2
0.1
0.7
0.01
100
100
100
single
single
single
5.2
Objective Function
The optimization of grain size, hardness, ultimate tensile strength was carried with the help of its mathematical equation. The mathematical equation is considered as objective function. The source code was developed using Turbo C. It is desirable to maximize hardness and ultimate tensile strength and minimize grain size. The objective function for minimizing grain size, as in Equation3 and maximizing hardness and ultimate tensile strength, as in Equation 4 & 5 were taken as their fitness functions. 6
Results and Discussions
Based on the results obtained in GA, the optimum values of PCMPAW input parameters and output responses like grain size, hardness and ultimate tensile strength are computed. The optimum grain size of 33.552 Microns is obtained for the welding input parameter combination of Peak Current 6.192 Amperes, Back Current 4.340 Amperes, Pulse rate 21.170 pulses/second and pulse width 50.070 %. The optimum hardness of 271.680 VHN is obtained for the welding input parameter combination of Peak Current 6.157 Amperes, Back Current 3.896 Amperes, Pulse rate 31.12 pulses/second and pulse width 42.60 %. The optimum ultimate tensile strength of 838.578 MPa is obtained for the welding input parameter combination of Peak Current 6.423Amperes, Back Current 4.371 Amperes, Pulse rate 22 pulses/second and pulse width 47.82 %. 7
Conclusions
Empirical models are developed for grain size, hardness and ultimate tensile strength for PCMPAW Inconel 625 sheets using RSM CCD design matrix. The weld quality parameters like grain size, hardness and ultimate tensile strength are optimized using GA by minimize grain size and maximize hardness and ultimate tensile strength. The optimum values obtained using GA are 33.552 Microns grain size, 271.680 VHN hardness and 838.578 MPa ultimate tensile strength. The optimum values obtained using GA is in good agreement with experimental values References
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5th International & 26th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12th–14th, 2014, IIT Guwahati, Assam, India
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